Epimorphisms in the Category of ℓ-Groups

Abstract

In the category of ℓ-groups, we introduce the concepts of Hopfian and generalized Hopfian ℓ-groups. An ℓ-group G is called Hopfian if every surjective ℓ-homomorphism f : G → G is an ℓ-isomorphism, and G is called generalized Hopfian if every surjective ℓ-homomorphism f : G → G has a small kernel in G. By an example we show that the class of generalized Hopfian ℓ-groups is a proper subclass of Hopfian ℓ-groups. In this paper, we establish some characterizations for them, which generalize some results in [9].